Bananas are sold in bunches at a grocery store and typically consist of 4-8 bananas per bunch. Suppose the weight of these bunches follows a normal distribution with a mean of 3.54 pounds and a standard deviation of 0.63 pounds. What is the probability that a randomly selected bunch of bananas will weigh less than 4.0 pounds?

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To find the probability that a bunch of bananas weighs less than 4.0 pounds, we use the Z-score formula: Z = (X - μ) / σ, where X is the value (4.0 pounds), μ is the mean (3.54 pounds), and σ is the standard deviation (0.63 pounds). Calculating the Z-score gives Z = (4.0 - 3.54) / 0.63 ≈ 0.7302. Looking up this Z-score in a standard normal distribution table or using a calculator gives a probability of approximately 0.7673, indicating that there's about a 76.73% chance a randomly selected bunch will weigh less than 4.0 pounds.

Bananas Are Sold in Bunches at a Grocery Store and Typically